The RStudio environment

Source: YaRrr! The Pirate’s Guide to R

R as a calculator

Common mathematic operations in R:

• + : addition
• - : subtraction
• / : division
• * : multiplication
• ^ : exponent
• sqrt() : square root
• exp() : exponential function

R as a calculator

2 + 2

[1] 4

3 - 1

[1] 2

2 * 6

[1] 12

4 / 2

[1] 2

sqrt(16)

[1] 4

R as a calculator

• To run a line of code just use CTRL + ENTER (that’s COMMAND + ENTER if you’re on a Mac)

• How would I ask R to divide 10 by 2?

10 / 2

[1] 5

• How would I ask R to calculate 5 to the 4th power?

5^4

[1] 625

R as a calculator

The R Calculator follows the PEMDAS rule:

Parentheseis, exponents, multiplication, division, addition, subraction from left to right

3 + 4 * 12

[1] 51

(3 + 4) * 12

[1] 84

Commenting

• Anything that you type after the “#” will be disregarded by R
• You can make notes to yourself and it will not interfere with your code

# This is a comment to my code
1 + 1

[1] 2

Creating Objects

• We use objects to store any kind of information in R
• Think of an object as a label for a piece of information
• We can save information as variables by using the assignment operator: <- or =
• General pattern:

a <- 2 + 2

• Now we can access this piece of information by ‘calling’ a

a 

[1] 4

Creating Objects

• R is case sensitive

A
# Error: object 'A' not found

• Objects can be overwritten

a <- 3
a

[1] 3

Labeling conventions

Numeric

class(18.9)

[1] "numeric"

my_number <- 13
class(my_number)

[1] "numeric"

is.numeric(my_number)

[1] TRUE

Character

Character data types must be surrounded by quotation marks

"student"

[1] "student"

myFirstCharacter <- "myFirstCharacter"
myFirstCharacter

[1] "myFirstCharacter"

• What happens if you don’t surround a character data type with quotation marks?

student
# Error: object 'student' not found

• Without quotation marks, R thinks this is an object label.

Logical

• There are only two options TRUE and FALSE

• They must be in all caps

true <- FALSE
true == TRUE

[1] FALSE

• You could also abbreviate TRUE to T and FALSE to F (not recommended)

Vectors

• Vectors allow saving multiple pieces of information to an object

• The individual values within a vector are called “elements”

• To do this we can use the c() function

• This function combines different pieces of information together

c(1, 2, 3, 4)

[1] 1 2 3 4

(1, 2, 3, 4)
# Error: unexpected ',' in "(1,"

Vectors

• We can save these pieces of information to an object

first_vector <- c(1, 2, 3, 4)

• We can look at this object by calling it through the object label

first_vector

[1] 1 2 3 4

• Can you guess the class of first_vector?

class(first_vector)

[1] "numeric"

Vectors

• We saved four pieces of information (four numbers) to the vector

• We can check the number of elements in a vector with the lenght() function

length(first_vector)

[1] 4

• A vector is a one-dimensional collection of information

• All the elements must be the same type

second_vector <- c(1, 2, 3, "four")

second_vector

[1] "1"    "2"    "3"    "four"

class(second_vector)

[1] "character"

Subsetting vectors

• To pull out one element from a vector that has multiple elements, we need to subset the vector

• Use square brackets [] after the label name with the element number we would like to recover inside the brackets

• myvector[1]

Subsetting vectors

• What if I want to pull out the third element from a vector?

second_vector[3]

[1] "3"

• We can save this as a new object

third_element <- second_vector[3]
third_element

[1] "3"

• We can also pull out multiple elements at once

second_vector[c(2, 3, 4)]

[1] "2"    "3"    "four"

Functions in R

• Functions are pre-written pieces of code that accomplish some task

• Rather than writing out the code to do this task, we can call a function by its label and it will complete that task

• Let’s say I wanted to calculate the mean (or average) of our numeric vector

(1 + 2 + 3 + 4) / 4 

[1] 2.5

Functions in R

• What if first_vector had 100 numbers not 4?

• Or what if you had 100 vectors and wanted to calculate the means of each one

• We could use the sum() function and the length() function

  • sum() will add up all the numbers in a vector
  • length() tells you how many elements are in a vector

sum(first_vector)/length(first_vector)

[1] 2.5

• Or we could use the mean() function

mean(first_vector)

[1] 2.5

Functions in R

Arguments

• Arguments are the information we give the function so it can carry out its task

• A function can have multiple arguments

• functionLabel(argument1, argument2, argument3)

• For the mean() function, the first argument was the data or the number we wanted the mean of

Functions in R

• round() will round whatever number you give in the first argument

round(3.666)

[1] 4

• What if I want it to round the number to the second decimal point?

• We can add another argument

round(3.666, 2) 

[1] 3.67

# The second argument tells it how many decimal points to round to

Functions in R

• Each argument has a label

• Sometimes we don’t use them for convenience, but it is helpful specially if you’re dealing with a function with many arguments

round(x = 3.666, digits = 2)

[1] 3.67

• If you use labels, the order of the arguments don’t matter

round(digits = 2, x = 3.666)

[1] 3.67

Functions in R

• What happens if we write the digits argument first without the labels?

round(2, 3.666)

[1] 2

• When you don’t use labels, the order really matters

• To learn more about a pre-built function and its arguments, type ?function_name() in the console (e.g., ?round()) to find the help page of that function

• Or you can press tab once your cursor is within the function parenthesis

Functions in R

• Another useful function is class()

• The class function will tell you what kind of data type

class(first_vector)

[1] "numeric"

class(second_vector)

[1] "character"

Types of data structure

1- Vector

2- Matrix

3- Array

4- Data frame

5- List

Matrix

• Two-dimensional dataset (has columns and rows) of one data type

• matrix(data, nrow, ncol, byrow)

m <- matrix(data = c(1:6), # The matrix will contain elements 1, 2, 3, 4, 5, 6
            nrow = 2, # this matrix will have two rows
            ncol = 3, # this matrix will have three columns
            byrow = TRUE) # we fill the elements by the row
m

     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6

• What happens if you change byrow = FALSE ?

Matrix

• dim() tells you the dimension of a matrix

• First element is number of rows, second element is number of columns

dim(m)

[1] 2 3

Matrix

• We can also create a matrix by combining vectors

vec1 <- 1:5
vec2 <- 6:10

• We can use the cbind() function to make each vector their own column in a matrix

col_matrix <- cbind(vec1, vec2)
col_matrix

     vec1 vec2
[1,]    1    6
[2,]    2    7
[3,]    3    8
[4,]    4    9
[5,]    5   10

Matrix

• Or we can use the rbind() function to make each vector their own row in a matrix

row_matrix <- rbind(vec1, vec2)
row_matrix

     [,1] [,2] [,3] [,4] [,5]
vec1    1    2    3    4    5
vec2    6    7    8    9   10

Data frames

• Allow you to have multiple data types

• We can use the data.frame() function to create a data frame

• Each argument is a different column

• We can also add labels to each column

dat <-  data.frame(
  schoolyear = c("Freshman", "Sophomore","Freshman"), 
  height = c(152, 171.5, 165), 
  weight = c(81,93, 78),
  age = c(18,20,19)
)

Subsetting Two-Dimensional Objects

• We’ve used square brackets [] to subset vectors

• We can use square brackets [] to subset two-dimensional objects like a matrix or data frame

• twoDimObject[row#, column#]

Subsetting Two-Dimensional Objects

• If I want to subset the element in row 3 and column 2

dat[3, 2]

[1] 165

• If I want to subset the entire 3rd column

dat[, 3]

[1] 81 93 78

Subsetting Two-Dimensional Objects

• I could also subset by column name

dat[, "weight"] # this subsets all the rows from the weight column

[1] 81 93 78

dat[1, "weight"] # this subsets the first row from the weight column

[1] 81

• If we just want to subset a column we can use the $ operator: twoDimObject$ColumnName

dat$schoolyear

[1] "Freshman"  "Sophomore" "Freshman" 

Central tendency: Mean, Median, and Mode

• These are the 3 most common measures of central tendency

• They are used to describe a distribution of observations (e.g., all the grades on an exam) in one number that best represents that distribution

• Suppose we asked a bunch of UC Davis students how many hours per week they spent watching Netflix, and how many hours they spent exercising during Winter break:

netflix <- c(2, 6, 1, 7, 2, 4, 11, 40, 7, 0, 3, 4, 5, 2, 15)
exercise <- c(2, 2, 6, 2, 12, 45, 8, 3, 2, 6, 4, 0, 1, 3, 0)

Central tendency: Mean, Median, and Mode

• How many observations are in each variable?

length(netflix)

[1] 15

length(exercise)

[1] 15

• Let’s take a look at the average time each student spent on these activities:

mean(netflix, na.rm = TRUE) # use the argument na.rm = TRUE to ignore missing values 

[1] 7.266667

mean(exercise, na.rm = TRUE)

[1] 6.4

• Unsurprisingly, students exercised less than they watched netflix, on average.

Central tendency: Mean, Median, and Mode

• But is the mean a good representation of these data?

• Take a look again at the values and see if you find something odd

netflix

 [1]  2  6  1  7  2  4 11 40  7  0  3  4  5  2 15

exercise

 [1]  2  2  6  2 12 45  8  3  2  6  4  0  1  3  0

• One person is watching Netflix 40h a week

• Another exercised 45h per week

Central tendency: Mean, Median, and Mode

• When we have outliers, sometimes the median is a better representation of the data

• Remember, the median is the middle value of your data, after you have ordered it

median(exercise, na.rm = TRUE)

[1] 3

median(netflix, na.rm = TRUE)

[1] 4

Central tendency: Mean, Median, and Mode

• Sometimes, we can’t do arithmetic on the data we have

• If we had asked our 15 participants what their favorite flavor of ice cream was, we would not be able to describe that distribution using a mean or a median. We would have to use the mode

• The mode is just the most frequent value

Central tendency: Mean, Median, and Mode

• R doesn’t have a function for because it is not very frequently used, so we use the table() function

• table() gives you the number of times each element shows up in an object

table(netflix)

netflix
 0  1  2  3  4  5  6  7 11 15 40 
 1  1  3  1  2  1  1  2  1  1  1 

• You can use the sort() function on the result of the table function to order it

sort(table(exercise))

exercise
 1  4  8 12 45  0  3  6  2 
 1  1  1  1  1  2  2  2  4 

Spread: Variance and Standard Deviation

• Do all the students exercise about the same? Or do some students exercise a lot while others don’t?

• How are the observations spread out around the mean or median?

• We’re gonna look at two different kinds that are related: Variance and standard deviation

Spread: Variance

1. Calculate the mean

mean(exercise, na.rm = TRUE)

[1] 6.4

2. Find the distance from each observation to the mean

exercise - mean(exercise, na.rm = TRUE)

 [1] -4.4 -4.4 -0.4 -4.4  5.6 38.6  1.6 -3.4 -4.4 -0.4 -2.4 -6.4 -5.4 -3.4 -6.4

• Let’s save that!

diffs <- exercise - mean(exercise, na.rm = TRUE)

Spread: Variance

3. Square the differences

diffs_sq <- diffs^2

4. Sum everything and divide by N-1

sum(diffs_sq)/(length(exercise) - 1)

[1] 124.4

• We can check our answers using var()

var(exercise, na.rm = TRUE)

[1] 124.4

Spread: Standard deviation

• To get the standard deviation, we just get the square root of the variance:

ex_var <- var(exercise, na.rm = TRUE)
sqrt(ex_var)

[1] 11.15347

• Or, R has a sd() function:

sd(exercise, na.rm = TRUE)

[1] 11.15347

• We often prefer to use the standard deviation, because its units are the same units of our variable

Relationships between variables: correlation and covariance

• In our imaginary example, each person gave us two bits of information, exercise and netflix hours

• Let’s organize our data into a dataframe to better keep track of it:

df <- data.frame(Netflix = netflix, 
                 Exercise = exercise, 
                 stringsAsFactors = FALSE) 
df

   Netflix Exercise
1        2        2
2        6        2
3        1        6
4        7        2
5        2       12
6        4       45
7       11        8
8       40        3
9        7        2
10       0        6
11       3        4
12       4        0
13       5        1
14       2        3
15      15        0

If you are in RStudio, you can look at df by clicking on it, using View(), typing it in the console or using functions like head() and tail(). Can you tell what those do?

head(df)

  Netflix Exercise
1       2        2
2       6        2
3       1        6
4       7        2
5       2       12
6       4       45

tail(df)

   Netflix Exercise
10       0        6
11       3        4
12       4        0
13       5        1
14       2        3
15      15        0

It’s also a good idea to plot your data

• This helps you get a general idea for what your data looks like, and to see if there is anything weird going on

• To make a scatterplot, we can use plot() function in R

plot(x = df$Netflix, y = df$Exercise)

We can make our plot look prettier changing the axis labels, and even giving our plot a title

plot(df$Netflix, df$Exercise, xlab = "Hours Spent Watching Netflix", #changes the x-axis label
     ylab = "Hours Spent Exercising", # changes the y-axis label
     main = "Plot of Time Spent Watching Netflix vs. Exercising over Break") # gives your plot a title

Covariance

• What if we wanted to quantify this relation? We can use the covariance and correlation!

• The covariance between two variables is a measure of how the two variables change together

• It only makes sense if there’s some connection between the two variables

• It resembles the variance, but instead of squared differences from the mean, we multiply these differences from the mean by each other

Covariance

1. Get the differences from the mean for each variable:

diff_nfx <- df$Netflix - mean(df$Netflix, na.rm = TRUE)
diff_ex <- df$Exercise - mean(df$Exercise, na.rm = TRUE)
# you can check this is right -- the differences will sum to 0 (or very close to it)
sum(diff_ex)

[1] -3.552714e-15

2. Multiply them by each other

mult_diffs <- diff_nfx * diff_ex

Covariance

3. Sum all these multiplied differences

sum_diffs <- sum(mult_diffs, na.rm = TRUE)

4. Divide by N - 1

cov_NetEx <- sum_diffs/14
cov_NetEx

[1] -15.18571

• We see that the covariance is negative, indicating that the Netflix and Exercise variables are inversely related to each other

Covariance

• You can verify this yourself by using the cov() function

cov_NetEx_2 <- cov(df$Netflix, df$Exercise, use = "complete.obs")
cov_NetEx_2

[1] -15.18571

• For cov(), the use = "complete.obs" argument acts similarly to na.rm = TRUE: it will only use data from people who gave an answer to both Netflix and exercise

Correlation

• We don’t know how strong is this association because covariances have arbitrary scales based on the scales of the original variables

• We don’t know how big they could get so we don’t know if this value is large or small

• Correlations can only range between -1 and 1, so they’re easier to interpret

Correlation

• We’ll standardize the covariance to get a correlation

• Standardizing in this case means dividing by the variables’ standard deviations:

sd_N <- sd(df$Netflix, na.rm = TRUE)
sd_E <- sd(df$Exercise, na.rm = TRUE)

• We divide the covariance by the product of the variances to get a correlation:

cov_NetEx/(sd_N*sd_E)

[1] -0.1377893

• And we can check this using the cor() function:

cor(df$Netflix, df$Exercise, use = "complete.obs")

[1] -0.1377893

cor(df$Netflix, df$Exercise, use = "complete.obs")

[1] -0.1377893

Since the correlation ranges between -1 and 1, we can say something about the strength of this relation

• Based on some rules of thumb we can say there is a weak negative relation between watching Netflix and exercise

• What is considered strong vs. weak can depend on the area of research you’re in

• Next week: statistical test to see whether this correlation is significantly different from 0 or not!